算法导论第九章:中位数和顺序统计量-全部代码实现

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        //9.2-4用例
        int A[] = {3,2,9,0,7,5,4,8,6,1};
        System.out.println(main.RANDOMIZED_SELECT(A, 0, A.length-1, 3));
        //9.3-6
        main.k_QUANTITIES(A, 3);
        //9.3-7找出接近中位数的k个元素:利用线性查找+DFS搜索
        //思考题9-1

    }

    //最优得到最小值
    public int MINIMUM(int[] A) {
        int MIN = A[0];
        for (int i = 1; i < A.length; i++) {
            if (A[i] < MIN) {
                MIN = A[i];
            }
        }
        System.out.println(MIN);
        return MIN;
    }

//    期望为线性时间的选择算法(快速排序+比较)
    private int RANDOMIZED_PARTITION(int[] A, int p, int r) {
        int i = (int) (Math.random() * (r - p) + p + 1);
        int temp = A[i];
        A[i] = A[r];
        A[r] = temp;
        return PARTITION(A, p, r);
    }
    private int PARTITION(int[] A, int p, int r) {
        int curr = A[r];
        int i = p;
        int t = 0;
        for (int j = p; j < r; j++) {
            if (A[j] <= curr) {
                A[r] = A[i];
                A[i] = A[j];
                A[j] = A[r];
                i++;
            }
        }
        A[r] = A[i];
        A[i] = curr;
        return i;
    }
//    递归版本
//    public int RANDOMIZED_SELECT(int A[], int p, int r, int i) {
//     if (p==r) return A[p];
//     else {
//         int q = RANDOMIZED_PARTITION(A, p, r);
//         if (i-1==q) return A[q];
//         else if (i-1<q) return RANDOMIZED_SELECT(A, p, q - 1, i);
//         else return RANDOMIZED_SELECT(A, q+1, r, i);
//        }
//    }

    //循环版本
    public int RANDOMIZED_SELECT(int A[], int p, int r, int i) {
        while (p!=r) {
                int q = RANDOMIZED_PARTITION(A, p, r);
                if (i-1==q) return A[q];
                else if (i-1<q) return RANDOMIZED_SELECT(A, p, q - 1, i);
                else return RANDOMIZED_SELECT(A, q+1, r, i);
            }
        return A[p];
    }

    //k分位数
    public void k_QUANTITIES_SUB(int[] A, int p, int r, int pos[], int f, int e, int quantiles[]) {
        if (f + 1 > e) return;
        int mid = (f + e) / 2;
        int q = RANDOMIZED_SELECT(A, p, r, pos[mid]);
        int val = q;
        quantiles[mid] = val;
        int k = q - p + 1;
        for (int i = mid; i < e; i++) {
            pos[i] = pos[i] - k;
        }
        k_QUANTITIES_SUB(A, q + 1, r, pos, mid + 1, e, quantiles);
    }

    public int[] k_QUANTITIES(int[] A, int k) {
        int num = A.length / k;
        int mod = A.length % k;
        int []pos = new int[k];
        for (int i = 0; i < mod; i++) {
            pos[i] = pos[i] + 1;
        }
        for (int i = 1; i < k; i++) {
            pos[i] = pos[i] + pos[i - 1];
        }
        int[] quantiles = new int[k];
        k_QUANTITIES_SUB(A, 0, A.length, pos, 0, pos.length, quantiles);
        for (int i :
                quantiles) {
            System.out.println(i);
        }
        return quantiles;
    }
}